{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Designing Nonlinear Kalman Filters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .output_wrapper, .output {\n",
       "            height:auto !important;\n",
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       "        }\n",
       "        .output_scroll {\n",
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       "        }\n",
       "        </style>\n",
       "    "
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Author's note: I was initially planning to have a design nonlinear chapter that compares various approaches. This may or may not happen, but for now this chapter has no useful content and I suggest not reading it. **"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the Kalman filter reasonably tracks the ball. However, as already explained, this is a silly example; we can predict trajectories in a vacuum with arbitrary precision; using a Kalman filter in this example is a needless complication."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kalman Filter with Air Drag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will dispense with the step 1, step 2, type approach and proceed in a more natural style that you would use in a non-toy engineering problem. We have already developed a Kalman filter that does excellently at tracking a ball in a vacuum, but that does not incorporate the effects of air drag into the model. We know that the process model is implemented with $\\textbf{F}$, so we will turn our attention to that immediately.\n",
    "\n",
    "Notionally, the computation that $\\textbf{F}$ computes is\n",
    "\n",
    "$$x' = Fx$$\n",
    "\n",
    "With no air drag, we had\n",
    "\n",
    "$$\n",
    "\\mathbf{F} = \\begin{bmatrix}\n",
    "1 & \\Delta t & 0 & 0 & 0 \\\\\n",
    "0 & 1 & 0 & 0 & 0 \\\\\n",
    "0 & 0 & 1 & \\Delta t & \\frac{1}{2}{\\Delta t}^2 \\\\\n",
    "0 & 0 & 0 & 1 & \\Delta t \\\\\n",
    "0 & 0 & 0 & 0 & 1\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which corresponds to the equations\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "x &= x + v_x \\Delta t \\\\\n",
    "v_x &= v_x \\\\\n",
    "\\\\\n",
    "y &= y + v_y \\Delta t + \\frac{a_y}{2} {\\Delta t}^2 \\\\\n",
    "v_y &= v_y + a_y \\Delta t \\\\\n",
    "a_y &= a_y\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the section above we know that our new Euler equations must be\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "x &= x + v_x \\Delta t \\\\\n",
    "v_x &= v_x \\\\\n",
    "\\\\\n",
    "y &= y + v_y \\Delta t + \\frac{a_y}{2} {\\Delta t}^2 \\\\\n",
    "v_y &= v_y + a_y \\Delta t \\\\\n",
    "a_y &= a_y\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Realistic 2D Position Sensors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The position sensor in the last example are not very realistic. In general there is no 'raw' sensor that provides (x,y) coordinates. We have GPS, but GPS already uses a Kalman filter to create a filtered output; we should not be able to improve the signal by passing it through another Kalman filter unless we incorporate additional sensors to provide additional information. We will tackle that problem later. \n",
    "\n",
    "Consider the following set up. In an open field we put two transmitters at a known location, each transmitting a signal that we can detect. We process the signal and determine  how far we are from that signal, with some noise. First, let's look at a visual depiction of that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "circle1=plt.Circle((-4, 0), 5, color='#004080', \n",
    "                   fill=False, linewidth=20, alpha=.7)\n",
    "circle2=plt.Circle((4, 0), 5, color='#E24A33', \n",
    "                   fill=False, linewidth=5, alpha=.7)\n",
    "\n",
    "fig = plt.gcf()\n",
    "ax = fig.gca()\n",
    "\n",
    "plt.axis('equal')\n",
    "plt.xlim((-10, 10))\n",
    "plt.ylim((-10, 10))\n",
    "\n",
    "plt.plot ([-4, 0], [0, 3], c='#004080')\n",
    "plt.plot ([4, 0], [0, 3], c='#E24A33')\n",
    "plt.text(-4, -.5, \"A\", fontsize=16, horizontalalignment='center')\n",
    "plt.text(4, -.5, \"B\", fontsize=16, horizontalalignment='center')\n",
    "\n",
    "ax.add_artist(circle1)\n",
    "ax.add_artist(circle2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I have attempted to show transmitter A, drawn in red, at (-4,0) and a second one B, drawn in blue, at (4,0). The red and blue circles show the range from the transmitters to the robot, with the width illustrating the effect of the $1\\sigma$ angular error for each transmitter. Here I have given the blue transmitter more error than the red one. The most probable position for the robot is where the two circles intersect, which I have depicted with the red and blue lines. You will object that we have two intersections, not one, but we will see how we deal with that when we design the measurement function.\n",
    "\n",
    "This is a very common sensor set up. Aircraft still use this system to navigate, where it is called DME (Distance Measuring Equipment). Today GPS is a much more common navigation system, but I have worked on an aircraft where we integrated sensors like this into our filter along with the GPS, INS, altimeters, etc. We will tackle what is called *multi-sensor fusion* later; for now we will just address this simple configuration.\n",
    "\n",
    "The first step is to design our state variables. We will assume that the robot is traveling in a straight direction with constant velocity. This is unlikely to be true for a long period of time, but is acceptable for short periods of time. This does not differ from the previous problem - we will want to track the values for the robot's position and velocity. Hence,\n",
    "\n",
    "$$\\mathbf{x} = \n",
    "\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}$$\n",
    "\n",
    "The next step is to design the state transition function. This also will be the same as the previous problem, so without further ado,\n",
    "\n",
    "$$\n",
    "\\mathbf{x}' = \\begin{bmatrix}1& \\Delta t& 0& 0\\\\0& 1& 0& 0\\\\0& 0& 1& \\Delta t\\\\ 0& 0& 0& 1\\end{bmatrix}\\mathbf{x}$$\n",
    "\n",
    "The next step is to design the control inputs. We have none, so we set ${\\mathbf{B}}=0$.\n",
    "\n",
    "The next step is to design the measurement function $\\mathbf{z} = \\mathbf{Hx}$. We can model the measurement using the Pythagorean theorem.\n",
    "\n",
    "$$\n",
    "z_a = \\sqrt{(x-x_A)^2 + (y-y_A)^2} + v_a\\\\[1em]\n",
    "z_b = \\sqrt{(x-x_B])^2 + (y-y_B)^2} + v_b\n",
    "$$\n",
    "\n",
    "where $v_a$ and $v_b$ are white noise.\n",
    "\n",
    "We see an immediate problem. The Kalman filter is designed for linear equations, and this is obviously nonlinear. In the next chapters we will look at several ways to handle nonlinear problems in a robust way, but for now we will do something simpler. If we know the approximate position of the robot than we can linearize these equations around that point. I could develop the generalized mathematics for this technique now, but instead let me just present the worked example to give context to that development."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of computing $\\mathbf{H}$ we will compute the partial derivative of $\\mathbf{H}$ with respect to the robot's position $\\mathbf{x}$. You are probably familiar with the concept of partial derivative, but if not, it just means how $\\mathbf{H}$ changes with respect to the robot's position. It is computed as the partial derivative of $\\mathbf{H}$ as follows:\n",
    "\n",
    "$$\\frac{\\partial \\mathbf{h}}{\\partial \\mathbf{x}} = \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial h_1}{\\partial x_1} & \\frac{\\partial h_1}{\\partial x_2} &\\dots \\\\\n",
    "\\frac{\\partial h_2}{\\partial x_1} & \\frac{\\partial h_2}{\\partial x_2} &\\dots \\\\\n",
    "\\vdots & \\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Let's work the first partial derivative. We want to find\n",
    "\n",
    "$$\\frac{\\partial }{\\partial x} \\sqrt{(x-x_A)^2 + (y-y_A)^2}\n",
    "$$\n",
    "\n",
    "Which we compute as\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\frac{\\partial h_1}{\\partial x} &= ((x-x_A)^2 + (y-y_A)^2))^\\frac{1}{2} \\\\\n",
    "&= \\frac{1}{2}\\times 2(x-x_a)\\times ((x-x_A)^2 + (y-y_A)^2))^{-\\frac{1}{2}} \\\\\n",
    "&= \\frac{x_r - x_A}{\\sqrt{(x_r-x_A)^2 + (y_r-y_A)^2}} \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "We continue this computation for the partial derivatives of the two distance equations with respect to $x$, $y$, $dx$ and $dy$, yielding\n",
    "\n",
    "$$\\frac{\\partial\\mathbf{h}}{\\partial\\mathbf{x}}=\n",
    "\\begin{bmatrix}\n",
    "\\frac{x_r - x_A}{\\sqrt{(x_r-x_A)^2 + (y_r-y_A)^2}} & 0 & \n",
    "\\frac{y_r - y_A}{\\sqrt{(x_r-x_A)^2 + (y_r-y_A)^2}} & 0 \\\\\n",
    "\\frac{x_r - x_B}{\\sqrt{(x_r-x_B)^2 + (y_r-y_B)^2}} & 0 &\n",
    "\\frac{y_r - y_B}{\\sqrt{(x_r-x_B)^2 + (y_r-y_B)^2}} & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "That is pretty painful, and these are very simple equations. Computing the Jacobian can be extremely difficult or even impossible for more complicated systems. However, there is an easy way to get Python to do the work for you by using the SymPy module [1]. SymPy is a Python library for symbolic mathematics. The full scope of its abilities are beyond this book, but it can perform algebra, integrate and differentiate equations, find solutions to differential equations, and much more. We will use it to compute our Jacobian!\n",
    "\n",
    "First, a simple example. We will import SymPy, initialize its pretty print functionality (which will print equations using LaTeX). We will then declare a symbol for NumPy to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\phi$"
      ],
      "text/plain": [
       "\\phi"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "from sympy import init_printing\n",
    "init_printing(use_latex='mathjax')\n",
    "\n",
    "phi, x = sympy.symbols('\\phi, x')\n",
    "phi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how we use a latex expression for the symbol `phi`. This is not necessary, but if you do it will render as LaTeX when output. Now let's do some math. What is the derivative of $\\sqrt{\\phi}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{2 \\sqrt{\\phi}}$"
      ],
      "text/plain": [
       " 1  \n",
       "────\n",
       "2⋅√φ"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.diff('sqrt(phi)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can factor equations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(\\phi - 1\\right) \\left(\\phi^{2} + 1\\right)$"
      ],
      "text/plain": [
       "        ⎛ 2    ⎞\n",
       "(φ - 1)⋅⎝φ  + 1⎠"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.factor('phi**3 -phi**2 + phi - 1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SymPy has a remarkable list of features, and as much as I enjoy exercising its features we cannot cover them all here. Instead, let's compute our Jacobian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{x - x_{a}}{\\sqrt{\\left(x - x_{a}\\right)^{2} + \\left(y - y_{a}\\right)^{2}}} & 0 & \\frac{y - y_{a}}{\\sqrt{\\left(x - x_{a}\\right)^{2} + \\left(y - y_{a}\\right)^{2}}} & 0\\\\\\frac{x - x_{b}}{\\sqrt{\\left(x - x_{b}\\right)^{2} + \\left(y - y_{b}\\right)^{2}}} & 0 & \\frac{y - y_{b}}{\\sqrt{\\left(x - x_{b}\\right)^{2} + \\left(y - y_{b}\\right)^{2}}} & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡           x - xₐ                           y - yₐ              ⎤\n",
       "⎢ ──────────────────────────   0   ──────────────────────────   0⎥\n",
       "⎢    _______________________          _______________________    ⎥\n",
       "⎢   ╱         2           2          ╱         2           2     ⎥\n",
       "⎢ ╲╱  (x - xₐ)  + (y - yₐ)         ╲╱  (x - xₐ)  + (y - yₐ)      ⎥\n",
       "⎢                                                                ⎥\n",
       "⎢          x - x_b                          y - y_b              ⎥\n",
       "⎢────────────────────────────  0  ────────────────────────────  0⎥\n",
       "⎢   _________________________        _________________________   ⎥\n",
       "⎢  ╱          2            2        ╱          2            2    ⎥\n",
       "⎣╲╱  (x - x_b)  + (y - y_b)       ╲╱  (x - x_b)  + (y - y_b)     ⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import symbols, Matrix\n",
    "phi = symbols('\\phi')\n",
    "phi\n",
    "\n",
    "x, y, xa, xb, ya, yb, dx, dy = symbols('x y x_a x_b y_a y_b dx dy')\n",
    "\n",
    "H = Matrix([[sympy.sqrt((x-xa)**2 + (y-ya)**2)], \n",
    "            [sympy.sqrt((x-xb)**2 + (y-yb)**2)]])\n",
    "\n",
    "state = Matrix([x, dx, y, dy])\n",
    "H.jacobian(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a nutshell, the entry (0,0) contains the difference between the x coordinate of the robot and transmitter A's x coordinate divided by the distance between the robot and A. (2,0) contains the same, except for the y coordinates of the robot and transmitters. The bottom row contains the same computations, except for transmitter B. The 0 entries account for the velocity components of the state variables; naturally the range does not provide us with velocity.\n",
    "\n",
    "The values in this matrix change as the robot's position changes, so this is no longer a constant; we will have to recompute it for every time step of the filter.\n",
    "\n",
    "If you look at this you may realize that this is just a computation of x/dist and y/dist, so we can switch this to a trigonometic form with no loss of generality:\n",
    "\n",
    "$$\\frac{\\partial\\mathbf{h}}{\\partial\\mathbf{x}}=\n",
    "\\begin{bmatrix}\n",
    "-\\cos{\\theta_A} & 0 & -\\sin{\\theta_A} & 0 \\\\\n",
    "-\\cos{\\theta_B} & 0 & -\\sin{\\theta_B} & 0\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "However, this raises a huge problem. We are no longer computing $\\mathbf{H}$, but $\\Delta\\mathbf{H}$, the change of $\\mathbf{H}$. If we passed this into our Kalman filter without altering the rest of the design the output would be nonsense. Recall, for example, that we multiply $\\mathbf{Hx}$ to generate the measurements that would result from the given estimate of $\\mathbf{x}$ But now that $\\mathbf{H}$ is linearized around our position it contains the *change* in the measurement function. \n",
    "\n",
    "We are forced, therefore, to use the *change* in $\\mathbf{x}$ for our state variables. So we have to go back and redesign our state variables. \n",
    "\n",
    ">Please note this is a completely normal occurrence in designing Kalman filters. The textbooks present examples like this as *fait accompli*, as if it is trivially obvious that the state variables needed to be velocities, not positions. Perhaps once you do enough of these problems it would be trivially obvious, but at that point why are you reading a textbook? I find myself reading through a presentation multiple times, trying to figure out why they made a choice, finally to realize that it is because of the consequences of something on the next page. My presentation is longer, but it reflects what actually happens when you design a filter. You make what seem reasonable design choices, and as you move forward you discover properties that require you to recast your earlier steps. As a result, I am going to somewhat abandon my **step 1**, **step 2**, etc.,  approach, since so many real problems are not quite that straightforward."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If our state variables contain the velocities of the robot and not the position then how do we track where the robot is? We can't. Kalman filters that are linearized in this fashion use what is called a *nominal trajectory* - i.e. you assume a position and track direction, and then apply the changes in velocity and acceleration to compute the changes in that trajectory. How could it be otherwise? Recall the graphic showing the intersection of the two range circles - there are two areas of intersection. Think of what this would look like if the two transmitters were very close to each other - the intersections would be two very long crescent shapes. This Kalman filter, as designed, has no way of knowing your true position from only distance measurements to the transmitters. Perhaps your mind is already leaping to ways of working around this problem. If so, stay engaged, as later sections and chapters will provide you with these techniques. Presenting the full solution all at once leads to more confusion than insight, in my opinion. \n",
    "\n",
    "So let's redesign our *state transition function*. We are assuming constant velocity and no acceleration, giving state equations of\n",
    "$$\n",
    "\\dot{x}' = \\dot{x} \\\\\n",
    "\\ddot{x}' = 0 \\\\\n",
    "\\dot{y}' = \\dot{y} \\\\\n",
    "\\dot{y}' = 0$$\n",
    "\n",
    "This gives us the the *state transition function* of\n",
    "\n",
    "$$\n",
    "\\mathbf{F} = \\begin{bmatrix}0 &1 & 0& 0\\\\0& 0& 0& 0\\\\0& 0& 0& 1\\\\ 0& 0& 0& 0\\end{bmatrix}$$\n",
    "\n",
    "A final complication comes from the measurements that we pass in. $\\mathbf{Hx}$ is now computing the *change* in the measurement from our nominal position, so the measurement that we pass in needs to be not the range to A and B, but the *change* in range from our measured range to our nominal position. \n",
    "\n",
    "There is a lot here to take in, so let's work through the code bit by bit. First we will define a function to compute $\\frac{\\partial\\mathbf{h}}{\\partial\\mathbf{x}}$ for each time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sin, cos, atan2\n",
    "\n",
    "def H_of(pos, pos_A, pos_B):\n",
    "    \"\"\" Given the position of our object at 'pos' in 2D, and two \n",
    "    transmitters A and B at positions 'pos_A' and 'pos_B', return \n",
    "    the partial derivative of H\n",
    "    \"\"\"\n",
    "\n",
    "    theta_a = atan2(pos_a[1] - pos[1], pos_a[0] - pos[0])\n",
    "    theta_b = atan2(pos_b[1] - pos[1], pos_b[0] - pos[0])\n",
    "\n",
    "    return np.array([[0, -cos(theta_a), 0, -sin(theta_a)],\n",
    "                     [0, -cos(theta_b), 0, -sin(theta_b)]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to create our simulated sensor. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "\n",
    "class DMESensor(object):\n",
    "    def __init__(self, pos_a, pos_b, noise_factor=1.0):\n",
    "        self.A = pos_a\n",
    "        self.B = pos_b\n",
    "        self.noise_factor = noise_factor\n",
    "        \n",
    "    def range_of(self, pos):\n",
    "        \"\"\" returns tuple containing noisy range data to A and B\n",
    "        given a position 'pos'\n",
    "        \"\"\"\n",
    "        \n",
    "        ra = math.sqrt((self.A[0] - pos[0])**2 + (self.A[1] - pos[1])**2)\n",
    "        rb = math.sqrt((self.B[0] - pos[0])**2 + (self.B[1] - pos[1])**2)\n",
    "        \n",
    "        return (ra + randn()*self.noise_factor, \n",
    "                rb + randn()*self.noise_factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we are ready for the Kalman filter code. I will position the transmitters at x=-100 and 100, both with y=-20. This gives me enough space to get good triangulation from both as the robot moves. I will start the robot at (0,0) and move by (1,1) each time step. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.book_plots as bp\n",
    "from filterpy.kalman import KalmanFilter\n",
    "import math\n",
    "import numpy as np\n",
    "\n",
    "pos_a = (100, -20)\n",
    "pos_b = (-100, -20)\n",
    "\n",
    "f1 = KalmanFilter(dim_x=4, dim_z=2)\n",
    "\n",
    "f1.F = np.array ([[0, 1, 0, 0],\n",
    "                  [0, 0, 0, 0],\n",
    "                  [0, 0, 0, 1],\n",
    "                  [0, 0, 0, 0]], dtype=float)\n",
    "\n",
    "f1.R *= 1.\n",
    "f1.Q *= .1\n",
    "\n",
    "f1.x = np.array([[1, 0, 1, 0]], dtype=float).T\n",
    "f1.P = np.eye(4) * 5.\n",
    "\n",
    "# initialize storage and other variables for the run\n",
    "count = 30\n",
    "xs, ys = [], []\n",
    "pxs, pys = [], []\n",
    "\n",
    "# create the simulated sensor\n",
    "d = DMESensor(pos_a, pos_b, noise_factor=3.)\n",
    "\n",
    "# pos will contain our nominal position since the filter does not\n",
    "# maintain position.\n",
    "pos = [0, 0]\n",
    "\n",
    "for i in range(count):\n",
    "    # move (1,1) each step, so just use i\n",
    "    pos = [i, i]\n",
    "    \n",
    "    # compute the difference in range between the nominal track\n",
    "    # and measured ranges\n",
    "    ra,rb = d.range_of(pos)\n",
    "    rx,ry = d.range_of((pos[0] + f1.x[0, 0], pos[1] + f1.x[2, 0]))\n",
    "    z = np.array([[ra - rx], [rb - ry]])\n",
    "\n",
    "    # compute linearized H for this time step\n",
    "    f1.H = H_of (pos, pos_a, pos_b)\n",
    "\n",
    "    # store stuff so we can plot it later\n",
    "    xs.append(f1.x[0, 0]+i)\n",
    "    ys.append(f1.x[2, 0]+i)\n",
    "    pxs.append(pos[0])\n",
    "    pys.append(pos[1])\n",
    "    \n",
    "    # perform the Kalman filter steps\n",
    "    f1.predict()\n",
    "    f1.update(z)\n",
    "\n",
    "bp.plot_filter(xs, ys)\n",
    "bp.plot_track(pxs, pys)\n",
    "plt.legend(loc=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearizing the Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have seen an example of linearizing the Kalman filter we are in a position to better understand the math. \n",
    "\n",
    "We start by assuming some function $\\mathbf f$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: A falling Ball"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**author's note: ignore this section for now. **\n",
    "\n",
    "In the **Designing Kalman Filters** chapter I first considered tracking a ball in a vacuum, and then in the atmosphere. The Kalman filter performed very well for vacuum, but diverged from the ball's path in the atmosphere. Let us look at the output; to avoid littering this chapter with code from that chapter I have placed it all in the file `ekf_internal.py'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.ekf_internal as ekf\n",
    "ekf.plot_ball()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can artificially force the Kalman filter to track the ball by making $Q$ large. That would cause the filter to mistrust its prediction, and scale the kalman gain $K$ to strongly favor the measurments. However, this is not a valid approach. If the Kalman filter is correctly predicting the process we should not 'lie' to the filter by telling it there are process errors that do not exist. We may get away with that for some problems, in some conditions, but in general the Kalman filter's performance will be substandard.\n",
    "\n",
    "Recall from the **Designing Kalman Filters** chapter that the acceleration is\n",
    "\n",
    "$$a_x = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_x \\\\\n",
    "a_y = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_y- g\n",
    "$$\n",
    "\n",
    "These equations will be *very* unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n",
    "\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\ddot{y} &= \\frac{0.0034ge^{-y/20000}\\dot{y}^2}{2\\beta} - g \\\\\n",
    "\\ddot{x} &= \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta}\n",
    "\\end{aligned}$$\n",
    "\n",
    "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is still nonlinear, so we need to linearize this equation at the current state point. If our state is position and velocity, we need an equation for some arbitrarily small change in $\\mathbf{x}$, like so:\n",
    "\n",
    "$$ \\begin{bmatrix}\\Delta \\dot{x} \\\\ \\Delta \\ddot{x} \\\\ \\Delta \\dot{y} \\\\ \\Delta \\ddot{y}\\end{bmatrix} = \n",
    "\\large\\begin{bmatrix}\n",
    "\\frac{\\partial \\dot{x}}{\\partial x} & \n",
    "\\frac{\\partial \\dot{x}}{\\partial \\dot{x}} & \n",
    "\\frac{\\partial \\dot{x}}{\\partial y} & \n",
    "\\frac{\\partial \\dot{x}}{\\partial \\dot{y}} \\\\ \n",
    "\\frac{\\partial \\ddot{x}}{\\partial x} & \n",
    "\\frac{\\partial \\ddot{x}}{\\partial \\dot{x}}& \n",
    "\\frac{\\partial \\ddot{x}}{\\partial y}& \n",
    "\\frac{\\partial \\dot{x}}{\\partial \\dot{y}}\\\\\n",
    "\\frac{\\partial \\dot{y}}{\\partial x} & \n",
    "\\frac{\\partial \\dot{y}}{\\partial \\dot{x}} & \n",
    "\\frac{\\partial \\dot{y}}{\\partial y} & \n",
    "\\frac{\\partial \\dot{y}}{\\partial \\dot{y}} \\\\ \n",
    "\\frac{\\partial \\ddot{y}}{\\partial x} & \n",
    "\\frac{\\partial \\ddot{y}}{\\partial \\dot{x}}& \n",
    "\\frac{\\partial \\ddot{y}}{\\partial y}& \n",
    "\\frac{\\partial \\dot{y}}{\\partial \\dot{y}}\n",
    "\\end{bmatrix}\\normalsize\n",
    "\\begin{bmatrix}\\Delta x \\\\ \\Delta \\dot{x} \\\\ \\Delta \\dot{y} \\\\ \\Delta \\ddot{y}\\end{bmatrix}$$\n",
    "\n",
    "The equations do not contain both an x and a y, so any partial derivative with both in it must be equal to zero. We also know that $\\large\\frac{\\partial \\dot{x}}{\\partial x}\\normalsize = 0$ and that  $\\large\\frac{\\partial \\dot{x}}{\\partial \\dot{x}}\\normalsize = 1$, so our matrix ends up being\n",
    "\n",
    "$$\\mathbf{F} = \\begin{bmatrix}0&1&0&0 \\\\\n",
    "\\frac{0.0034e^{-x/22000}\\dot{x}^2g}{44000\\beta}&0&0&0\n",
    "\\end{bmatrix}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{aligned}\\ddot{x} &= -\\frac{1}{2}C_d\\rho A \\dot{x}\\\\\n",
    "\\ddot{y} &= -\\frac{1}{2}C_d\\rho A \\dot{y}-g\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.abc import *\n",
    "from sympy import *\n",
    "\n",
    "init_printing(pretty_print=True, use_latex='mathjax')\n",
    "\n",
    "x1 = (0.0034*g*exp(-x/22000)*((x)**2))/(2*b) - g\n",
    "\n",
    "x2 = (a*g*exp(-x/c)*(Derivative(x)**2))/(2*b) - g\n",
    "\n",
    "#pprint(x1)\n",
    "#pprint(Derivative(x)*Derivative(x,n=2))\n",
    "#pprint(diff(x2, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** orphan text\n",
    "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. **\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] http://sympy.org\n"
   ]
  }
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